Sure. In fact, this is the operating system used for the automated testing of the Nano RP2040 Connect's boards platform:
The core library of the "Mbed OS Nano Boards" platform of the Nano RP2040 Connect is based on Mbed OS. So when you follow the standard instructions for getting started with the Nano RP2040 Connect, you are ending up running Mbed OS on your board. You can still use the standard Arduino core API, since Mbed OS API is wrapped in it, or if you like, or you also have the option of using Mbed OS API directly.
Give it a try and let us know if you have any problems.